Sistema ETD

Archivio digitale delle tesi discusse presso l'Università di Pisa

 

Tesi etd-06272016-104810


Tipo di tesi
Tesi di laurea magistrale
Autore
GIOFFRE', STEFANO
URN
etd-06272016-104810
Titolo
Fine study of a limit equation arising in general relativity
Struttura
MATEMATICA
Corso di studi
MATEMATICA
Commissione
relatore Prof. Malchiodi, Andrea
correlatore Benci, Vieri
controrelatore Alberti, Giovanni
Parole chiave
  • relatività generale
  • analisi geometrica
Data inizio appello
15/07/2016;
Consultabilità
parziale
Data di rilascio
15/07/2019
Riassunto analitico
In this thesis we deal with the Einstein problem in general relativity,
treating in particular the vacuum case. Using a trick developed by
Choquet-Bruhat and Lichnerowicz, the well known "conformal method", one
can write the vacuum Einstein equations as a couple of differential
equations, called constraint equations: a Yamabe-like scalar equation with
a nonlinearity term and a vector equation coupled to the first. In an
article written in 2011 by Gicquaud, Humbert, Dahl the authors proved a theorem
which states that either the constraint equations admit solutions or
another differential equation, a limit one, admits a non-trivial solution.
Our aim is to present this problem, explain the main ideas and present an
attempt to prove non-existence theorems for the limit equations based on a
fine analysis of the proof made in the article.
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